If terms of an arithmetic sequence are added together an arithmetic series is formed.
2 + 4 + 6 + 8 is a finite arithmetic series
2 + 4 + 6 + 8 + ... is an infinte arithmetic series
To find the sum of the first n terms of an arithmetic sequence use the formula:
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Sum of first n terms of arithmetic sequence d = common difference |
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OR
An equivalent formula involving the last term, l
| Sum of first n terms of arithmetic sequence |
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Example 1
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What is the sum of the first 15 terms of the arithmetic sequence: 3, 6, 9, 12, ... |
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Example 2
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The first term of an arithmetic sequence is 5 and the last term is 250. The sum of this series is 1020. How many terms does it have? |
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Example 3
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An athlete does 20 press-ups on the first day of a training routine. On the second day she does 24 press-ups and on the third day 28 press-ups. If she follows this pattern for 30 days, how many press-up will she have done altogether? |
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